Method and apparatus for low power chip-to-chip communications with constrained isi ratio

ABSTRACT

An efficient communications apparatus is described for a vector signaling code to transport data and optionally a clocking signal between integrated circuit devices. Methods of designing such apparatus and their associated codes based on a new metric herein called the “ISI Ratio” are described which permit higher communications speed, lower system power consumption, and reduced implementation complexity.

This application is a Continuation of and claims priority under 35 USC§120 to U.S. application Ser. No. 14/816,899, filed Aug. 3, 2015, whichis a Continuation of U.S. application Ser. No. 14/612,241, filed Feb. 2,2015, entitled “Method and Apparatus for Low Power Chip-to-ChipCommunications with Constrained ISI Ratio” which is a non-provisionalapplication claiming priority under 35 USC §119 to U.S. ProvisionalApplication 61/934,803, entitled “Method for Code Evaluation using ISIRatio,” filed on Feb. 2, 2014, all of which are hereby incorporatedherein by reference in their entirety for all purposes.

REFERENCES

The following references are herein incorporated by reference in theirentirety for all purposes:

-   U.S. Patent Publication 2011/0268225 of application Ser. No.    12/784,414, filed May 20, 2010, naming Harm Cronie and Amin    Shokrollahi, entitled “Orthogonal Differential Vector Signaling”    (hereinafter “Cronie I”);-   U.S. patent application Ser. No. 13/030,027, filed Feb. 17, 2011,    naming Harm Cronie, Amin Shokrollahi and Armin Tajalli, entitled    “Methods and Systems for Noise Resilient, Pin-Efficient and Low    Power Communications with Sparse Signaling Codes”, hereinafter    identified as [Cronie II];-   U.S. patent application Ser. No. 14/158,452, filed Jan. 17, 2014,    naming John Fox, Brian Holden, Peter Hunt, John D Keay, Amin    Shokrollahi, Richard Simpson, Anant Singh, Andrew Kevin John    Stewart, and Giuseppe Surace, entitled “Chip-to-Chip Communication    with Reduced SSO Noise”, hereinafter identified as [Fox I];-   U.S. patent application Ser. No. 14/178,051, filed Feb. 11, 2014,    naming John Fox, Brian Holden, Peter Hunt, John D Keay, Amin    Shokrollahi, Richard Simpson, Andrew Kevin John Stewart, Giuseppe    Surace, and Roger Ulrich, entitled “Methods and Systems for High    Bandwidth Chip-to-Chip Communications Interface”, hereinafter    identified as [Fox II];-   U.S. patent application Ser. No. 13/842,740, filed Mar. 15, 2013,    naming Brian Holden, Amin Shokrollahi and Anant Singh, entitled    “Methods and Systems for Skew Tolerance in and Advanced Detectors    for Vector Signaling Codes for Chip-to-Chip Communication”,    hereinafter identified as [Holden I];-   U.S. Provisional Patent Application 61/839,360, filed Jun. 23, 2013,    naming Amin Shokrollahi, entitled “Vector Signaling with Reduced    Receiver Complexity” (hereinafter “Shokrollahi I”);-   U.S. Provisional Patent Application No. 61/839,360, filed Jun. 23,    2013, naming Amin Shokrollahi, entitled “Vector Signaling Codes with    Reduced Receiver Complexity”, hereinafter identified as [Shokrollahi    II].-   U.S. Provisional Patent Application No. 61/946,574, filed Feb. 28,    2014, naming Amin Shokrollahi, Brian Holden, and Richard Simpson,    entitled “Clock Embedded Vector Signaling Codes”, hereinafter    identified as [Shokrollahi III].-   U.S. Provisional Patent Application No. 62/015,172, filed Jul. 10,    2014, naming Amin Shokrollahi and Roger Ulrich, entitled “Vector    Signaling Codes with Increased Signal to Noise Characteristics”,    hereinafter identified as [Shokrollahi IV].-   U.S. patent application Ser. No. 13/895,206, filed May 15, 2013,    naming Roger Ulrich and Peter Hunt, entitled “Circuits for Efficient    Detection of Vector Signaling Codes for Chip-to-Chip Communications    using Sums of Differences”, hereinafter identified as [Ulrich I].-   U.S. Provisional Patent Application No. 62/026,860, filed Jul. 21,    2014, naming Roger Ulrich and Amin Shokrollahi, entitled “Bus    Reversible Orthogonal Differential Vector Signaling Codes”,    hereinafter identified as [Ulrich II].-   U.S. patent application Ser. No. 14/315,306, filed Jun. 25, 2014,    naming Roger Ulrich, entitled “Multilevel Driver for High Speed    Chip-to-Chip Communications”, hereinafter identified as [Ulrich    III].

The following additional references to prior art have been cited in thisapplication:

-   U.S. Pat. No. 7,053,802, filed Apr. 22, 2004 and issued May 30,    2006, naming William Cornelius, entitled “Single-Ended Balance-Coded    Interface with Embedded-Timing”, hereinafter identified as    [Cornelius];-   U.S. Pat. No. 8,649,460, filed Mar. 11, 2010 and issued Feb. 11,    2014, naming Frederick Ware and Jade Kizer, entitled “Techniques for    Multi-Wire Encoding with an Embedded Clock”, hereinafter identified    as [Ware].

FIELD OF THE INVENTION

The present invention relates generally to the field of communications,and more particularly to the transmission and reception of signalscapable of conveying information within and between devices.

BACKGROUND

In communication systems, a goal is to transport information from onephysical location to another. It is typically desirable that thetransport of this information is reliable, is fast and consumes aminimal amount of resources. One common information transfer medium isthe serial communications link, which may be based on a single wirecircuit relative to ground or other common reference, or multiple suchcircuits relative to ground or other common reference. A common exampleuses singled-ended signaling (“SES”). SES operates by sending a signalon one wire, and measuring the signal relative to a fixed reference atthe receiver. A serial communication link may also be based on multiplecircuits used in relation to each other. A common example of the latteruses differential signaling (“DS”). Differential signaling operates bysending a signal on one wire and the opposite of that signal on amatching wire. The signal information is represented by the differencebetween the wires, rather than their absolute values relative to groundor other fixed reference.

There are a number of signaling methods that maintain the desirableproperties of DS while increasing pin efficiency over DS. Vectorsignaling is a method of signaling. With vector signaling, a pluralityof signals on a plurality of wires is considered collectively althougheach of the plurality of signals might be independent. Each of thecollective signals is referred to as a component and the number ofplurality of wires is referred to as the “dimension” of the vector. Insome embodiments, the signal on one wire is entirely dependent on thesignal on another wire, as is the case with DS pairs, so in some casesthe dimension of the vector might refer to the number of degrees offreedom of signals on the plurality of wires instead of exactly thenumber of wires in the plurality of wires.

Any suitable subset of a vector signaling code denotes a “subcode” ofthat code. Such a subcode may itself be a vector signaling code. Withbinary vector signaling, each component or “symbol” of the vector takeson one of two possible values. With non-binary vector signaling, eachsymbol has a value that is a selection from a set of more than twopossible values. The set of all values required to represent all symbolsis called the “alphabet” of the code. Thus, as examples, a binary vectorsignaling code requires at least an alphabet of two values, while aternary vector signaling code requires at least an alphabet of threevalues. When transmitted as physical signals on a communications medium,symbols may be represented by particular physical values appropriate tothat medium; as examples, in one embodiment a voltage of 150 mV mayrepresent a “+1” symbol and a voltage of 50 mV may represent a “−1”symbol, while in another embodiment “+1” may be represented by 800 mVand “−1” as −800 mV.

A vector signaling code, as described herein, is a collection C ofvectors of the same length N, called codewords. The ratio between thebinary logarithm of the size of C and the length N is called thepin-efficiency of the vector signaling code. The Orthogonal DifferentialVector Signaling or ODVS codes of [Cronie I], [Cronie II], [Fox I],[Shokrollahi I], [Shokrollahi II], and [Shokrollahi III] are examples ofvector signaling codes, and are used herein for descriptive purposes.

Inter-symbol interference (ISI) is the distortion of a symbol to bedecoded at the receiver by the residual effects of symbols previouslysent through the system. This effect is mainly due to properties of theunderlying communication channel, and often is the limitingcharacteristic precluding higher speed or lower error communications.Well-known examples of channels vulnerable to ISI include wirelesscommunications with multipath interference and band-limited channels inwired systems. Since ISI degradation is deterministic, it is advisableto cancel its effect before trying to decode the current symbol toobtain its embedded information. In some cases, a sequence ofpreviously-sent symbols that constructively combine to maximize theirimpact on the detection margin of the current symbol. Since theseworst-case symbol patterns usually occur with a high probabilitycompared to the target error-rate of the system, their effect and how toquantify and minimize their destructive behavior is a major concern inthe design of communication systems. Beyond such ad-hoc identificationof problematic patterns, there is no reliable metric to assess theimpact of ISI on communications system performance, nor to suggestchannel or coding modifications to mitigate such effects.

One way to combat the ISI problem is to use equalizers which render theequivalent channel ISI-free. Equalizers are functional processing blocksor circuits that try to invert the channel in such a way that thetransmitted data at each symbol interval becomes (ideally) independentof the other symbols sent through the system. In aSerializer-Deserializer (SerDes) design, FIR (Finite Impulse Responsefiltering) and CTLE (Continuous Time Linear Equalization) are twowell-known linear equalization methods used respectively at thetransmitter and receiver sides of the system while DFE (DecisionFeedback Equalization) is a receiver-side non-linear equalizationmethod. Other equalization methods such as the Tomlinson-Harashimaprecoding method are also known to practitioners of the field. Suchpre-coding is often equivalent to equalization at the transmitter. Onone hand, equalizers can be expensive in terms of implementationcomplexity, power consumption, and calibration requirements, especiallyin multi-gigabit/s communication systems. Thus, there is a need for bothmetrics that accurately reflect the impact of ISI on communicationssystem performance, and for channel processing solutions that mitigateISI effects in an efficient, high performance manner.

BRIEF DESCRIPTION

An efficient communications apparatus is described for a vectorsignaling code to transport data and optionally a clocking signalbetween integrated circuit devices. Methods of designing such apparatusand their associated codes based on a new metric herein called the “ISIRatio” are described which permit higher communications speed, lowersystem power consumption, and reduced implementation complexity.

BRIEF DESCRIPTION OF FIGURES

FIG. 1 illustrates an embodiment of a communications system inaccordance with the invention.

FIG. 2 shows the case of differential signaling on two wires sending onebit per symbol.

FIG. 3 shows the case of PAM-4 signaling on two wires sending two bitsper symbol.

FIG. 4 shows the pulse response of the example channel used for thesimulations herein.

FIG. 5 shows eye diagrams for the first case MIC embodiment of a P3receiver.

FIG. 6 shows eye diagrams for the second case MIC embodiment of a P3receiver.

FIGS. 7A through 7E show eye diagrams for the five sub-channels of a5b6w code receiver.

FIGS. 8A through 8C show eye diagrams for the three sub-channels of anENRZ code receiver.

FIGS. 9A and 9B show eye diagrams for the 4.5b5w code of [ShokrollahiI].

FIGS. 10A and 10B show eye diagrams for an 8b8w code.

FIG. 11 is a graph comparing performance of NRZ, PAM-4, and ENRZsignaling over the same channel model.

FIG. 12 shows an eye-diagram for NRZ as an example of common practicesignaling methods on this channel.

FIG. 13 shows the eye-diagrams for PAM-4 as an example of commonpractice signaling methods on this channel.

FIG. 14 is a block diagram of a Glasswing receiver.

FIG. 15 is a block diagram of a Glasswing receiver recovering anembedded clock.

FIG. 16 is a schematic of one embodiment of a multi-input comparatorwith input weights as defined by row 6 of the matrix of Eqn. 3, bothwith and without equalization.

FIG. 17 is a schematic of one alterative one embodiment of a multi-inputcomparator with input weights as defined by row 6 of the matrix of Eqn.3, both with and without equalization.

FIG. 18 is a schematic of one embodiment of a multi-input comparatorwith input weights as defined by row 3 of the matrix of Eqn. 3, bothwith and without equalization. With suitable substitution of wireinputs, it also may be used to embody the comparator of row 5 of thematrix of Eqn. 3.

FIG. 19 is a schematic of one alterative embodiment of a multi-inputcomparator with input weights as defined by row 3 of the matrix of Eqn.3, both with and without equalization. With suitable substitution ofwire inputs, it also may be used to embody the comparator of row 5 ofthe matrix of Eqn. 3.

FIG. 20 is a schematic of one embodiment of a multi-input comparatorwith input weights as defined by row 2 of the matrix of Eqn. 3, bothwith and without equalization. With suitable substitution of wireinputs, it also may be used to embody the comparator of row 4 of thematrix of Eqn. 3.

FIG. 21 is a block diagram of one embodiment of a Glasswing 5b6wtransmit driver.

FIG. 22 is a block diagram of one embodiment of a Glasswing 5b6w_10_5transmit driver.

FIG. 23 is a flow diagram of a transmission method.

FIG. 24 is a flow diagram of a reception method.

DETAILED DESCRIPTION

FIG. 1 illustrates an embodiment of a communication system in accordancewith the invention employing a vector signaling code. Source data totransmitter 110, herein illustrated as S₀, S₁, S₂, S₃, S₄ enters as asource data word 100 into encoder 112. The size of the source data wordmay vary and depends on the parameters of the vector signaling code. Theencoder 112 generates a codeword of the vector signaling code for whichthe system is designed. In operation, the codeword produced by encoder112 is used to control PMOS and NMOS transistors within driver 118,generating two, three, or more distinct voltages or currents on each ofthe N communication wires 125 of communications channel 120, torepresent the N symbols of the codeword. In the embodiment of FIG. 1,the size of the source data word is shown as five bits and the codewordsize is six symbols. Thus, communications channel 110 is shown as beingcomprised of six signal wires 125, each transporting one codewordsymbol. One familiar with the encoding arts may also describe this codeas having a block length of six (i.e. producing an output word of sixsymbols) and a code size of 32 (i.e. having 32 distinct codewords,sufficient to encode 5 binary bits of data.)

Within communications receiver 130, detector 132 reads the voltages orcurrents on wires 125, possibly including amplification, frequencycompensation, and common mode signal cancellation. In the presentexample, the received results 140, herein shown as R₀, R₁, R₂, R₃, R₄,are provided directly by detector 132, without need of optional decoder138.

As will be readily apparent, different codes may be associated withdifferent block sizes and different codeword sizes; for descriptiveconvenience and without implying limitation, the example of FIG. 1illustrates a system using an ODVS code capable of encoding five binarybit values for transmission over six wires, a so-called 5b6w code.

Depending on which vector signaling code is used, there may be nodecoder, or no encoder, or neither a decoder nor an encoder. Forexample, for the 8b8w code disclosed in [Cronie II], both encoder 112and decoder 138 exist. On the other hand, for the 5b6w code of thepresent example, an explicit decoder is unnecessary, as the system maybe configured such that detector 132 generates the received results 140directly.

The operation of the communications transmitter 110 and communicationsreceiver 130 have to be completely synchronized in order to guaranteecorrect functioning of the communication system. In some embodiments,this synchronization is performed by an external clock shared betweenthe transmitter and the receiver. Other embodiments may combine theclock function with one or more of the data channels, as in thewell-known Biphase encoding used for serial communications, or othermethods described herein.

Signaling in a Communications System

Signaling is a method of transmitting information over communicationchannels. Any form of mapping information (typically represented asbits) to physical quantities that are carried on the communicationchannel is referred to as signaling. In preferred embodiments,information to be conveyed on a communication channel is modulatedthrough a shaped pulse having a real-valued function of finite support.The signals transmitted on the wires are of the form

Σ_(i=−∞) ^(+∞) C _(i) P(t−iT)  [Eqn. 1]

where C_(i) is the codeword vector of length N (equal to the number ofwires), T is the temporal length of a unit interval (UI) of the pulserepresenting one transmitted value, and P is a function on the interval[0,T] defining the pulse shape used for modulation. The codewords C_(i)determine the information sent at every instance. The choice of the setto which the C_(i) belongs, together with the choice of the mappingbetween the information bits and the C_(i) determines the signalingmethod.Pulse amplitude modulation (PAM) is a method of signaling in which theC_(i) can take one of the values [−1, −1+2/(X−1), −1+4/(X−1), . . . ,1−4/(X−1), 1−2/(X−1), 1] representing equal amplitude intervals over theallowable signal range. This type of signaling is referred to as PAM-Xsignaling. Often (but not exclusively), X is a power of 2, and eachC_(i) carries log 2(X) (binary logarithm of X) information bits. In manyhigh-speed SerDes applications, X=2, though values such as X=4, X=8, orX=16 have also been proposed in various standards bodies.

It is well known to those of skill in the art that while PAM-X signalingleads to a higher ratio of transmitted bits per unit interval, it ismore susceptible to ISI than PAM-2. This is often falsely attributed tothe fact that in PAM-X signaling has more possible transition extents(i.e. changes in signal amplitude,) with the different amounts of timeneeded to traverse these extents leading to the increased ISI. Based onthis false premise, it has also often been suggested that any signalingmethod that uses an alphabet size larger than 2 will suffer from ISImore than PAM-2. However, we subsequently show the alphabet size doesnot directly impact ISI.

A vector signaling code, as described here, is a collection C of vectorsof the same dimension N, called codewords, a second collection Λ ofvectors of dimension N, called multi-input comparators (MIC's), and aset of “don't cares” wherein each don't care is a pair C_(i), λ, withC_(i) being an element of C and λ being an element of Λ. In operation,the coordinates of the elements of C are bounded, and we choose torepresent them by real numbers between −1 and 1.

In operation, a codeword is uniquely determined by the vector of thescalar products of that codeword with all the MIC's λ for which C_(i), λis not a don't care. If a pair C_(i), λ is not a don't care, we say thatC_(i) is active for MIC λ.

An example is provided as follows: the collection C of codewordsconsists of the 12 vectors obtained from the permutations of the vector(1,0,0,−1), the MIC's are the six vectors

-   -   (1,−1,0,0), (1,0,−1,0), (1,0,0,−1), (0,1,−1,0), (0,1,0,−1),        (0,0,1,−1)        and the set of don't cares are those pairs of codewords and        MIC's such that the scalar product of the MIC with the codeword        is zero. In other words, the don't cares are the pairs        ((1,0,0,−1), (0,1,−1,0)), ((1,0,−1,0), (0,1,0,−1)),        ((1,−1,0,0),(0,0,1,−1)), ((0,1,−1,0),(1,0,0,−1)),        ((0,1,0,−1), (1,0,−1,0)), ((0,0,1,−1),(1,−1,0,0)),        ((0,0,−1,1),(1,−1,0,0)), ((0,−1,1,0),(1,0,0,−1)),        ((0,−1,0,1),(1,0,−1,0)), ((−1,0,0,1),(0,1,−1,0)),        ((−1,0,1,0),(0,1,0,−1)), ((−1,1,0,0),(0,0,1,−1)).

In the following we will use interchangeably the interpretation of a MICbeing defined as a vector, and as a hyper-plane given by the set of allpoints orthogonal to this vector.

The ISI problem is examined from this signaling point of view with theintent to determine how to transfer data in a manner less sensitive tothe uncorrected residual ISI in the system. In situations where thedetection of signals is achieved using comparisons of signal values tofixed references or to one another, the ISI susceptibility shown to beprimarily determined by the signal levels observed at the output ofthese comparators, rather than by the signal levels observed on thewires themselves. We introduce the concept of the ISI-Ratio, a metricthat will help us quantify the effect of the ISI noise as a function ofthe signaling and the detection methods used. We will use this conceptto design vector signaling methods that are robust against ISI noise andwill show simulation results confirming this approach.

Receivers Using Multi-Input Comparators

As described in [Holden I], a practical embodiment of a multi-inputcomparator or MIC with coefficients a₀, a₁, . . . , a_(m-1) is asummation circuit that accepts as its input a vector (x₀, x₁, . . . ,x_(m-1)) from a plurality of signal conductors and outputs

Result=(a ₀ *x ₀ + . . . +a _(m-1) *x _(m-1))  (Eqn. 2)

where (x₀ . . . x_(m-1)) is the signal weight vector for the summationcircuit. In many embodiments, the desired output is a binary value, thusthe value Result is sliced with an analog comparator or other suchsignal slicer circuit to produce a binary decision output. Because thisis a common use case, the colloquial name of this circuit incorporatesthe term “comparator”, although other embodiments may apply thesummation result to a PAM-3 or PAM-4 slicer to obtain ternary orquaternary outputs, or indeed may retain the analog output of Eqn. 2 forfurther computation.

Receivers Described in Matrix Notation

Mathematically, the set of multi-input comparators comprising a codereceiver may be concisely described using matrix notation, with thecolumns of the matrix corresponding to consecutive elements of inputvector (x₀, x₁, . . . , x_(m-1)) i.e. the plurality of signal conductoror wire inputs carrying the vector signaling code, and each row of thematrix corresponding to the vector defining a particular multi-inputcomparator and its output. In this notation, the value of matrix elementcorresponds to the weight vector or set of scaling factors applied tothat column's input values by that row's multi-input comparator.

The matrix of Eqn. 3 describes one such set of multi-input comparatorscomprising a code receiver.

$\quad\begin{matrix}\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 0 & 0 & 0 & 0 \\\frac{1}{2} & \frac{1}{2} & {- 1} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {- 1} & 0 \\0 & 0 & 0 & \frac{1}{2} & \frac{1}{2} & {- 1} \\\frac{1}{3} & \frac{1}{3} & \frac{1}{3} & {- \frac{1}{3}} & {- \frac{1}{3}} & {- \frac{1}{3}}\end{matrix} & \left( {{Eqn}.\mspace{14mu} 3} \right)\end{matrix}$

In this embodiment, six input wires, represented by the six matrixcolumns, are processed by five multi-input comparators represented bymatrix rows 2-6. For purposes to be subsequently described, the firstmatrix row is comprised of all “1” values, creating a square 6×6 matrix.

As used herein, a matrix M such as that of Eqn. 3 is called “orthogonal”if M^(T)M=D that is, if the product of the matrix and its transpose is adiagonal matrix having non-zero values only on its diagonal. This is aweaker definition than commonly used, where the result is required to bethe identity matrix, i.e. having diagonal values equal to 1. Matrix Mmay be normalized to satisfy the stronger conventional orthogonalityrequirement, but as will subsequently be described such normalization isneither necessary nor desirable in practice.

Functionally, orthogonality requires that the vector of weights in a rowrepresenting a multi-input comparator be orthogonal to all other rows,and that each row representing a multi-input comparator sums to zero. Asthis implies the comparator outputs are also orthogonal (and thereforeindependent,) they represent distinct communications modes, hereindescribed as “sub-channels” of the Vector Signaling Code communicationssystem.

Given this modal interpretation, the initial row of the matrix may beseen to represent the common-mode communications channel over thetransmission medium. As it is desirable in a practical system for thereceiver to have common-mode rejection, the first row is set to all “1”values, maximizing the common mode contribution of each wire input tothis one matrix row. As by definition all rows of the matrix areorthogonal, it follows that no other matrix row (i.e. no receiveroutput) may then be impacted by common mode signals. Embodiments havingsuch common mode rejection need not implement a physical comparatorcorresponding to the first row of their descriptive matrix.

For avoidance of confusion, it is noted that all data communications inan ODVS system, including the state changes representing signals carriedin sub-channels, are communicated as codewords over the entire channel.An embodiment may associate particular mappings of input values tocodewords and correlate those mappings with particular detector results,as taught herein and by [Holden I] and [Ulrich I], but thosecorrelations should not be confused with partitions, sub-divisions, orsub-channels of the physical communications medium itself. Similarly,the concept of ODVS sub-channels is not limited by the exampleembodiment to a particular ODVS code, transmitter embodiment, orreceiver embodiment. Encoders and/or decoders maintaining internal statemay also be components of embodiments in accordance with the invention.Sub-channels may be represented by individual signals, or by statescommunicated by multiple signals.

[Shokrollahi II] describes methods of constructing orthogonal matricesthat may be utilized as described herein.

Generating ODVS Codes Corresponding to a Receiver Matrix

As described in [Cronie I] and [Cronie II], an Orthogonal DifferentialVector Signaling code may be constructed from a generator matrix bymultiplication of an input modulation vector of the form (0, a₁, a₂, . .. a_(n)) by the matrix M In the simplest case, each a_(i) of this vectoris the positive or negative of a single value, as example ±1,representing one bit of transmitted information.

Given our understanding of M as describing the various communicationsmodes of the system, it may readily be seen that multiplication of thematrix by such an input vector comprises excitation of the various modesby the of that vector, with the zeroth mode corresponding to common modetransmission not being excited at all. It will be obvious to onefamiliar with the art that transmission energy emitted in the commonmode is both unnecessary and wasteful in most embodiments. However, inat least one embodiment in accordance with the invention, a nonzeroamplitude for the common mode term is used to provide a nonzero bias orbaseline value across the communications channel.

It also may be seen that the various codewords of the code generatedusing this method represent linear combinations of the variousorthogonal communication modes. Without additional constraints beingimposed (e.g., for purposes of implementation expediency,) this methodresults in systems capable of communicating N−1 distinct sub-channelsover N wires, typically embodied as a N−1 bit/N wire system. The set ofdiscrete codeword values needed to represent the encoded values iscalled the alphabet of the code, and the number of such discretealphabet values is its alphabet size.

As a further example, the code generated by this method from the matrixof Eqn. 3 is shown in Table 1.

TABLE 1 ±[1, ⅓, −1/3, −1, −1/3, ⅓] ±[1, ⅓, −1/3, ⅓, −1, −1/3] ±[⅓, 1,−1/3, −1, −1/3, ⅓] ±[⅓, 1, −1/3, ⅓, −1, −1/3] ±[⅓, −1/3, 1, −1, −1/3, ⅓]±[⅓, −1/3, 1, ⅓, −1, −1/3] ±[ −1/3, ⅓, 1, −1, −1/3, ⅓] ±[ −1/3, ⅓, 1, ⅓,−1, −1/3] ±[1, ⅓, −1/3, −1, ⅓, −1/3] ±[1, ⅓, −1/3, ⅓, −1/3, −1] ±[⅓, 1,−1/3, −1, ⅓, −1/3] ±[⅓, 1, −1/3, ⅓, −1/3, −1] ±[⅓, −1/3, 1, −1, ⅓, −1/3]±[⅓, −1/3, 1, ⅓, −1/3, −1] ±[ −1/3, ⅓, 1, −1, ⅓, −1/3] ±[ −1/3, ⅓, 1, ⅓,−1/3, −1]

As may be readily observed, the alphabet of this code consists of thevalues +1, +⅓, −⅓, −1, thus this is a quaternary code (e.g. having analphabet size of four.) This code will subsequently be described hereinas the 5b6w or “Glasswing” code, and its corresponding receive matrix ofEqn. 3 as the “Glasswing receiver”.

Timing Information on a Sub-Channel

As an ODVS communications system must communicate each combination ofdata inputs as encoded transmissions, and the rate of such encodedtransmissions is of necessity constrained by the capacity of thecommunications medium, the rate of change of the data to be transmittedmust be within the Nyquist limit, where the rate of transmission ofcodewords represents the sampling interval. As one example, a binaryclock or strobe signal may be transmitted on an ODVS sub-channel, if ithas no more than one clock edge per codeword transmission.

An embodiment of an ODVS encoder and its associated line drivers mayoperate asynchronously, responding to any changes in data inputs. Otherembodiments utilize internal timing clocks to, as one example, combinemultiple phases of data processing to produce a single high-speed outputstream. In such embodiments, output of all elements of a codeword isinherently simultaneous, (absent any logic delay or other implementationconstrain,) thus a strobe or clock signal being transported on asub-channel of the code will be seen at the receiver as a data-alignedclock (e.g. with its transition edges occurring simultaneous to dataedges on other sub-channels of the same code.) Methods are well known inthe art to convert such a data-aligned clock into a delayed orcenter-of-eye-aligned clock, suitable for initiating sampling of datasub-channels in combination with the present invention. Such methods mayinclude introduction of a fixed time delay, adjustable time delay,delay-locked loop, etc.

ISI-Ratio

The ISI-Ratio is a measure of the sensitivity of a signaling scheme tothe inter-symbol interference in a communication system. It is in asense a measure for the deterioration of a signaling scheme due toresidual uncorrected ISI.

To formalize the above definition, assume that we have N communicationwires. At each Unit Interval (called UI in the following), the Encoderpicks one out of K possible codewords of length N (based on the bits tobe sent) and the drivers create voltages/currents proportional to thecoordinate values of the codeword and drive the wires with those values.Without implying limitation, we assume in this example that arectangular pulse shape P_(t) is used for the value on each wire. Thecodewords travel on the channel towards the receiver. On the receiverside, the wire values may pass through an equalizer and possibly a gainstage at the Rx front-end, and these new values are combined in(possibly) multiple linear ways in the comparator network to arrive at aset of decision values. As discussed before, the comparators may takelinear combinations of wire values and compare them against fixedreferences, or against other linear combinations of wire values. Thereceiver comparator network has M MIC's. The MIC's can be convenientlydescribed as “affine linear forms” on the wire values. In other words,to each MIC is associated a set of coefficients a₀, a₁, . . . , a_(n) Inoperation, the output of the MIC is the sign of the expression a₀+a₁x₁+. . . +a_(n)x_(n) where x₁, . . . , x_(n) are the values on wires 1, . .. , N, respectively, and −a₀ is the corresponding reference value. Wecall the MIC “central” if its reference value is 0. Otherwise we callthe MIC non-central. A central MIC is often also written as the vectorof the coefficients of its linear form, i.e., as [a₀, a₁, . . . ,a_(n)]. Central MIC's can be of two flavors: reference-less MIC's andreferenced MIC's. A reference-less MIC is a central MIC for which thesum of its coefficients is zero.

For example, in standard differential signaling, the MIC coefficientsare simply the pair [+1, −1] with the result compared against 0. This isa central reference-less MIC. In PAM-4 signaling, the same MIC is used,but two of the three MIC's have references. In other words, if thelargest signal value is 1 and the smallest signal value is −1, the MIC'sare given by the following 3 affine linear forms:

x ₁ −x ₂−⅔,x ₁ −x ₂ ,x ₁ −x ₂+⅔  [Eqn. 4]

In general, some of the coefficients of a MIC may be zero, in which casetheir corresponding inputs are simply discarded.

At times, it is advantageous to use a geometric view of a MIC, byconsidering a MIC as a hyper-plane in the N-dimensional Euclidean space.The MIC is then identified with the set of all vectors that evaluate to0 for that MIC. For example, for the MIC [1,−1] with reference 0 thehyper-plane is just the line x=y in the two-dimensional Euclidean plane.We will often and interchangeably identify MIC's with theircorresponding vectors, or their associated hyper-planes. In thisgeometric view, a MIC is central if its hyper-plane passes through theorigin, and it is non-central if not.

Each of the K codewords in the code can be interpreted as points in an Ndimensional Euclidean space. The task of the MIC's is to separate thepoints. A MIC that is not a don't care for two codewords separates thepoints if the points lie on opposite sides of the hyper-planecorresponding to the MIC.

FIGS. 2 and 3 show the case of differential and PAM-4 signaling on twowires sending one and two bits per symbol, respectively. In the case ofdifferential signaling, shown in FIG. 2, the hyper-plane is the line ofangle 45 degrees passing through the origin, and the codewords are thepoints with coordinates (1,−1) and (−1,1). These codewords are separatedby the hyper-plane, and they have equal distance from the hyper-plane.For PAM-4 signaling as shown in FIG. 3, the hyper-planes are the line ofangle 45 degrees passing through the origin, and the two translations ofthis line by the vectors (⅔, −⅔) and (−⅔, ⅔). The codewords are thepoints (1,−1), (⅓,−⅓), (−⅓, ⅓) and (−1,1), all lying on the lineperpendicular to the MIC's. As can be seen, the MIC's separate thecodewords.

We will show new signaling methods designed based on the ISI-Ratioconcept. The ISI-Ratio is defined for a MIC λ, with respect to the set Cof codewords. Let Δ_(m) be the set of codeword indices that are activefor MIC m (i.e., they are not don't cares for that MIC). In order toprecisely define the ISI-Ratio, we need to distinguish the central MIC's(where the hyper-plane passes through the origin) and non-central MICs(where the hyper-plane does not pass through the origin as in the twoMICs in the PAM-4 signaling) separately.

ISI-Ratio Calculation for Central MICs

Let d(C_(k),MIC_(m)) be the distance between codeword C_(k) and thehyper-plane representing MIC_(m). The ISI-Ratio for MIC_(m) is definedas:

$\begin{matrix}{{{ISIRatio}(m)} = {\frac{\max_{1 \leq k \leq K}{d\left( {C_{k},{MIC}_{m}} \right)}}{\min_{k \in \Delta_{m}}{d\left( {C_{k},{MIC}_{m}} \right)}}.}} & \left\lbrack {{Eqn}.\mspace{14mu} 5} \right\rbrack\end{matrix}$

Geometrically, the ISI-Ratio may be seen to be the ratio of the maximumdistance of any active codeword to the MIC hyper-plane, to the minimumdistance of any active codeword to the MIC hyper plane. If we computethis quantity for the signaling examples above, we obtain the followingnumbers:

Differential Signaling:

ISI-Ratio is 1 for the MIC.

PAM-4 Signaling:

ISI-Ratio is 3 for the middle MIC (which is central).

These values may be verified by examining the differential signalingcase of FIG. 2, where the two codeword points are equidistant from theMIC plane, representing a max/min distance ratio of 1. In the PAM-4signaling of FIG. 3, a ratio of 3:1 is seen in the distances of thefarthest to nearest codeword points to the central MIC plane.

Other examples will be presented addressing signaling design based onISI-Ratio.

ISI-Ratio Calculation for Non-Central MICs

Let d(C_(k),MIC_(m)) be the distance between codeword C_(k) and thehyper-plane representing the referenced MIC_(m). Denote by d₀(C_(k),MIC_(m)) the distance between the codeword C_(k) and the shifted versionof MIC_(m) passing through the origin. Then, the ISI-Ratio for thenon-central MIC_(m) is defined as:

$\begin{matrix}{{{ISIRatio}(m)} = {\frac{\max_{1 \leq k \leq K}{d_{0}\left( {C_{k},{MIC}_{m}} \right)}}{\min_{k \in \Delta_{m}}{d\left( {C_{k},{MIC}_{m}} \right)}}.}} & \left\lbrack {{Eqn}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

By this formula, the ISI-Ratio for the two non-central MICs of PAM-4signaling is also equal to 3. Therefore, the ISI-Ratio of all the MICsin a PAM-4 communication system is 3.

ISI-Ratio and Horizontal Eye-Opening

Each of the k codewords C_(k) k=1, . . . , K generates a pulse responseof its own at the output of MIC_(m) which is given by:

P _(m,k)(t)=Σ_(rx=1) ^(N)MIC_(m)(rx)[Σ_(tx=1) ^(N) C _(k)(tx)P(t)*h_(rx,tx)(t)]  Eqn. 7

Under the assumption that there is negligible crosstalk in the systemand the channels h_(i,t)(t) are all equal (=h(t)), the pulse responsegenerated by codeword K at the output of MIC_(m) is given by:

P _(m,k)(t)=[Σ_(i=1) ^(N)MIC_(m)(i)C _(k)(i)]P _(h)(t)  [Eqn. 8]

where P_(h)(t)=P(t)*h(t) is the pulse response of the system, includingall the linear equalizers, MIC_(m)(i) is the i-th coordinate of the m-thMIC, and C_(k)(i) is the i-th coordinate of the codeword C_(k). Assumingthat the MIC is central and its coefficients are normalized such thattheir sum of squares is equal to 1, the quantity |Σ_(i=1)^(N)MIC_(m)(i)C_(k)(i)| represents the distance between the codeword Kand the central hyper-plane representing MIC_(m). Note that theISI-Ratio is invariant under nonzero scalar multiplications of the MIC'sby arbitrary nonzero real numbers. Therefore, it can be assumed that thevectors representing the MIC's have norm 1 (i.e., the sum of squares oftheir coefficients is 1).

The signal at the output of MIC_(m) is the super-position of the pulseresponses P_(m,k)(t) shifted in time by integer multiples of the UIlength (=T) and for arbitrary choices of the codewords. Let us assumethat t₀ is the reference sampling time for the codeword C₀. At time t₀we have

r _(m)(t ₀)=Σ_(k) P _(m,k)(t ₀ −kT)=Σ_(k)[Σ_(i=1) ^(N)MIC_(m)(i)C_(k)(i)]P _(h)(t ₀ −kT).  [Eqn. 9]

For a central MIC, the receiver eye at the MIC output is closed for thesampling time t in which r_(m)(t) changes sign with respect to its signat t₀. This determines the horizontal opening of the eye at the MICoutput. For many communication systems, the goal is to achieve very lowdetection error rates at the receiver (e.g., less than 10⁻¹²) andtherefore, it is the worst-case codeword pattern that determines theeye-opening. The worst-case codeword pattern occurs when the codeword tobe detected is the closest codeword to the hyper-plane representingMIC_(m) (we call it C_(min)(m)) and the pre- and post-cursor codewordsare at the farthest distance (we call it C_(max)(m)) from thathyper-plane. Choosing these codewords, we can write:

$\begin{matrix}\begin{matrix}{{r_{m}\left( t_{0} \right)} = {{{d\left( {{C_{\min}(m)},{MIC}_{m}} \right)}{P_{h}\left( t_{0} \right)}} -}} \\{{\sum\limits_{k}\; {{d\left( {{C_{\max}(m)},{MIC}_{m}} \right)}{P_{h}\left( {t_{0} - {kT}} \right)}}}} \\{= {{d\left( {{C_{\min}(m)},{MIC}_{m}} \right)}\left\lbrack {{P_{h}\left( t_{0} \right)} - {{ISIRatio}*\Sigma_{k}{P_{h}\left( {t_{0} - {kT}} \right)}}} \right\rbrack}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 10} \right\rbrack\end{matrix}$

By changing the sampling phase t₀, the eye closes whenever the term

P _(h)(t ₀)−ISIRatio*Σ_(k) P _(h)(t ₀ −kT)  [Eqn. 11]

changes sign. The higher the ISI-Ratio for the signaling scheme, thebigger the residual ISI we see from the neighboring codewords and theeye will close sooner. Note that for a given pulse response P_(h)(t)(determined by the channel, equalizers, transmitter pulse-shape and thebaud-rate of the system), the horizontal opening depends only on theISI-Ratio of the underlying signaling scheme. The higher the ISI-Ratio,the smaller the horizontal opening of the eye.

For the case of non-central signaling, it is the distance to thereference of the MIC, denoted by ref(m) that determines the horizontalopening of the eye. Therefore, Eqn. 8 is changed to:

$\begin{matrix}\begin{matrix}{{r_{m}\left( t_{0} \right)} = {{\begin{matrix}{{\sum\limits_{i = 1}^{N}\; {{{MIC}_{m}(i)}{C_{\min}(i)}}} - {{{ref}(m)}{P_{h}\left( t_{0} \right)}} -} \\{\sum\limits_{k}\; {d_{0}\left( {{C_{\max}(m)},{MIC}_{m}} \right)}}\end{matrix}}{P_{h}\left( {t_{0} - {kt}} \right)}}} \\{= {{d\left( {{C_{\min}(m)},{MIC}_{m}} \right)}\left\lbrack {{P_{h}\left( t_{0} \right)} - {{ISIRatio}*\Sigma_{k}{P_{h}\left( {t_{0} - {kT}} \right)}}} \right\rbrack}}\end{matrix} & \left\lbrack {{Eqn}.\mspace{14mu} 12} \right\rbrack\end{matrix}$

again showing that the horizontal eye-opening is solely determined bythe ISI-Ratio of the underlying MIC.

Signaling Design Based on the ISI-Ratio Metric

Based on the discussion above, we can design signaling schemes based onthe ISI-Ratio concept. For purposes of description, examples are drawnfrom the domain of wire-line transmission systems, although nolimitation is implied.

As a first example, we wish to send b bits of information over achannel, thus requiring us to have at least 2^(b) codewords in oursignaling scheme. We have also the following considerations in ourdesign:

-   -   The dimension N is equal to the number of wires (i.e.        independent communications elements or sub-channels) in the        channel.    -   The codewords have all their coordinates in the range [−1, 1]        because of voltage swing constraints at the transmitter.

The goal is to find the codewords, the MICs, and the don't care pairs,such that the codewords can be distinguished by these MICs and themaximum ISI-Ratio of the MICs is minimized. As shown in the previoussection, the MIC with the highest ISI-Ratio will dominate and thehorizontal opening of its corresponding eye will determine the errorrate of the entire communication system.

In the following examples a 4-wire transmission line is used, withchannel characteristics based on the reference channel provide by TE(www.te.com) for 2 wires on a back-plane channel measured for the IEEE802.3bj standard (found online atwww-dot-ieee802.org/3/100GCU/public/channel.html). That describedchannel response was expanded to a 4 wire channel with crosstalk removedbetween wires. The baud rate was fixed at 8 GBaud per second. Acontinuous-time linear equalizer (CTLE) with equalization range between0 dB to 12 dB and a 3-tap filter at the transmitter were assumed, withequalizer settings optimized to obtain the best horizontal eye openings.The pulse response of the resulting channel is shown in FIG. 4.

As examples of common practice signaling methods on this channel, FIG.12 shows an eye-diagram for NRZ (throughput=4 Gbps/wire, horizontalopening=106.2 psec) and FIG. 13 shows the eye-diagrams for PAM-4(throughput=8 Gbps/wire, horizontal opening=40.0 psec) signaling.

A first embodiment of a vector signaling code design is called P3signaling, and uses 4 codewords (1, 0, −1), (−1, 0, 1), (0, 1, −1) and(0, −1, 1) to send 2 bits over 3 wires of the example channel. Weconsider the two following cases:

Case 1: We choose the MICs as (1, −1, 0) and (0, 1, −1). The outputs forthe two MICs on the four codewords are the values 1, −1, −1, 1 and 1,−1, 2, −2, respectively. It is obvious from examination that the twoMICs can distinguish the 4 codewords from each other. The ISI-Ratio forthe first MIC is 1 (horizontal opening=106.2 psec) while the ISI-Ratiofor the second MIC is 2 (horizontal opening=60 psec). The throughput is5.33 Gbps/wire. The eye-diagrams are shown in FIG. 5.

Case 2: We choose the MICs as (1, −1, 0) and (½, ½, −1). The outputs ofthe second MIC becomes 3/2, −3/2, 3/2, −3/2. The two MICs can stilldistinguish the codewords but the ISI_Ratio is 1 for both MIC's(horizontal opening=106.2 psec for both MICs). The throughput is 5.33Gbps/wire. The eye-diagrams are shown in FIG. 6.

This example confirms that MICs with the same ISI-Ratio on the samechannel under the same clock rate lead to approximately the samehorizontal eye openings, and that the right choice of the MICs iscrucial for the signal integrity of the transmission system.

A second embodiment of a signaling design utilizes linear coding; thatis, the signaling scheme is defined by means of a matrix-vector product.The vector contains the bits to be transmitted and the matrix definesthe transformation applied to the bits in order to generate thecodewords. In this scheme, one can in principle send N−1 bits over Nwires. The vector representing the bits is of the form (0, ±1, ±1, . . ., ±1). The coding matrix has the first row as all ones and the other N−1rows are orthogonal to first row and span the remaining(N−1)-dimensional subspace; thus, this is an orthogonal matrix aspreviously described herein. The MIC coefficients are found simply fromthe corresponding N−1 columns of the inverse of the coding matrix.

An interesting property of the linear coding scheme based on anorthogonal matrix is that the output of all the MICs are simply of theform ±1 and therefore the ISI-Ratio is guaranteed to be 1. As will beseen, this guarantee has a profound effect on communications systemperformance using such codes.

In a further embodiment, we can make use of the P3 code above and buildthe following Glasswing coding matrix to send 5 bits over 6 wires:

$\begin{matrix}{{{S \cdot A} = w}{{{where}\mspace{14mu} A} = \begin{bmatrix}1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 0 & 0 & 0 & 0 \\1 & 1 & {- 2} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {- 1} & 0 \\0 & 0 & 0 & 1 & 1 & {- 2} \\1 & 1 & 1 & {- 1} & {- 1} & {- 1}\end{bmatrix}}} & \left\lbrack {{Eqn}.\mspace{14mu} 13} \right\rbrack\end{matrix}$

and S=a row vector of information bits [0, S₀, S₁, S₂, S₃, S₄]representing antipodal weights (e.g., ±1 for logic bits 0, 1, oralternatively ±⅓), and w is the codeword vector to be transmitted [w₀,w₁, w₂, w₃, w₄, w₅]. If antipodal weights of ±1 are used, then thetransmitted codewords may then be normalized by a factor of ⅓ to resultin codewords having a quaternary alphabet of {±⅓, ±1}. Furthermore,because of the selection of the sub-channel code words of equation 13,the linear combinations of the sub-channel codes that form the codewordsthat are ultimately transmitted will provide a reduced alphabet ofcodeword elements. That is, at least one of the sub-channel code vectorshas a non-normalized magnitude and wherein the row-wise linearcombinations of the reduced-alphabet matrix provide a reduced alphabet.It may be observed that sub-channel code vectors having three non-zeroelements comprise a first non-zero element twice as large as each of asecond non-zero element and a third non-zero element, and a position ofthe first non-zero element is aligned to where only one othersub-channel codeword vector has a non-zero element.

The inverse matrix whose columns define the MIC coefficients is simplythe transpose of the matrix A of Eqn. 13 with appropriate normalization,and was previously described as Eqn. 3. The throughput is 6.66Gbps/wire. The eye-diagrams of this scheme are shown in FIG. 7A throughFIG. 7E. The horizontal opening is 106.2 psec for all the MICs. The fivebit over six wire or 5b6w code of Eqn. 13, MIC matrix of Eqn. 3, andcodewords of Table 1 will herein be called the “Glasswing” code.

A third embodiment of a signaling design also utilizes linear coding andis called Ensemble-NRZ or ENRZ. A full description of ENRZ may be foundin [Cronie I]. ENRZ has 8 codewords of the form ±perm(1, −⅓, −⅓, −⅓)where “perm” means all the permutations of the coefficients, and 3 MICsof the form (½, −½, ½, −½), (½, ½, −½, −½) and (½, −½, −½, ½), and cansend 3 bits over 4 wires per unit interval. The coding matrix is ascaled version of the 4×4-Hadamard matrix:

$\begin{matrix}{A = {\frac{1}{3}\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1\end{bmatrix}}} & \left\lbrack {{Eqn}.\mspace{14mu} 14} \right\rbrack\end{matrix}$

The scale factor ⅓ is chosen so that the final values are constrained tobe between −1 and 1. The throughput is 6 Gbps/wire. The eye-diagrams forENRZ signaling are shown in FIGS. 8A through 8C. The horizontal openingis 106.2 psec for the three MICs.

A fourth embodiment is a vector-signaling code design having theproperty of containing different MICs with different ISI-Ratios as wellas non-active codewords for the MICs. This category of codes allows thedesigner to provide codes with fewer number of MICs compared to thecodes with the same throughput and all ISI-Ratios equal. Moreover, as wesee in the following examples, the MICs with smaller ISI-Ratio aregenerally ones that make the linear combination on more wires comparedto the MICs with higher ISI-Ratios. Since these MICs provide morehorizontal opening, this property makes these MICs more tolerant tohigher skew when more wires are involved in the linear combination. Anexample of this design strategy is drawn from [Shokrollahi I], whichdescribes a code having 24 codewords of the form ±(perm(1,1,0,−1)|−1)where “perm” means all the permutations of the coefficients. This codecan send 4.5 bits over 5 wires in each unit interval. There are 7 MICsin this scheme, the first 6 are all the pairwise comparisons between thefirst four wires and all have ISI-Ratio 2. The last MIC has coefficients(¼, ¼, ¼, ¼, −1) and has ISI-Ratio 1. The throughput is 7.2 Gbps/wire.The eye-diagrams in s 9A and 9B show the wider horizontal opening of thelast MIC (FIG. 9B, horizontal opening=106.2 psec) compared to thepairwise comparator MICs with higher ISI-Ratios (FIG. 9A, horizontalopening=62.5 psec).

The final example embodiment is a code that sends 8 bits over 8 wiresusing 13 MICs. The codewords are of the form ±(perm(1,1,0,−1)perm(−1,−1,0,1)) where “perm” means all the permutations of thecoefficients. The MIC's are 6 pairwise comparators on the first fourwires, 6 pairwise comparators on the second four wires, and one MIC(1,1,1,1,−1,−1,−1,−1)/4. The last input MIC has ISI ratio of 1 whileeach of the pairwise comparator MICs has an ISI-Ratio of 2. Thethroughput is 8 Gbps/wire. The eye-diagrams are shown in FIGS. 10A and10B. The MIC with ISI-Ratio 1 has horizontal opening of 106.2 psec (FIG.10B) while the other MICs with ISI-Ratio 2 has horizontal opening of62.5 psec (FIG. 10A).

To allow direct comparison of these embodiments, we calculate thehorizontal eye openings for the previously described ENRZ, NRZ and PAM-4signaling schemes and then plot the relationship of horizontal eyeopening as a function of the throughput. The throughput values arenormalized for comparison purposes, as the required baud rate to obtainthe same throughput differ for each of these signaling schemes.

The result is shown in the graph of FIG. 11. Comparing NRZ and ENRZ, theISI-Ratio of both is equal to 1 while the baud rate of ENRZ is ⅔ that ofNRZ. Comparing PAM4 and ENRZ, the baud rate of ENRZ is 4/3 of PAM4, butits ISI-Ratio is 3 times smaller. Thus, the embodiment having the lowestISI-Ratio, ENRZ with its ISI-Ratio of 1, is the overall winner acrossthe throughput range, illustrating that low ISI-Ratio is a predictor ofgood communications system performance.

Normalizing Sub-Channel Gain

Performing a numerical analysis of the codes of Table 1 and the receiverdefined by the matrix of Eqn. 3, it may be observed that comparatorsdefined by matrix rows 1, 3, and 5 produce output values of ±⅔, whereasthe comparators defined by matrix rows 2 and 4 produce output values of±1. The loss in vertical eye opening compared to differential signalingis therefore 20*log₁₀(3)=˜9.5 dB. This output level variation is theresult of our loosened definition of orthogonality for the receivematrix, as the non-unity values of the diagonal M^(T)M=D representnon-unity gains for the corresponding sub-channels. As will be apparentto one familiar with the art, normalizing the matrix (i.e. scaling itselements such that the diagonal values are 1), will result in a systemhaving constant unity gain across all sub-channels. However, such knownnormalization methods may lead to suboptimal embodiments as the largenumber of distinct normalized coefficient values, in many casesincluding irrational values, are difficult to embody in a practicalsystem.

At least one embodiment retains the unnormalized matrix as exemplifiedby Eqn. 3 with its convenient-to-implement coefficient values, andinstead compensates for the variation of sub-channel amplitude bymodifying the input signal amplitudes modulating the varioussub-channel. For example, a hypothetical system having eightsub-channels of unity gain and one sub-channel of 0.8 gain willultimately be SNR limited by the latter output. Thus, increasing thelast sub-channel's transmission input to {+1.2, −1.2} rather than {+1,−1} will bring up the corresponding channel output. Alternatively,decreasing all other sub-channel inputs to {+0.8, −0.8} will lower thecorresponding channel outputs, such that all channels have equal outputlevels with less transmit power required.

This compensation technique is not without cost, however. As taught by[Shokrollahi IV], modifying the input vector in this manner leads to anincrease in the alphabet size needed (and thus, the number of discretesignal levels the transmitter must generate) to communicate thecodewords over the channel. [Shokrollahi IV] teaches numeric methods toselect suitable modulation amplitudes that result in closer matching ofsub-channel outputs with minimal expansion of the required alphabetsize.

Applying the procedure taught by [Shokrollahi IV], the optimal initialcode set for Glasswing is calculated to be (0, ±⅜, ±¼, ±⅜, ±¼, ±⅜) withthe corresponding code having an alphabet of size 10 given by (1, ⅞, ½,¼, ⅛, −⅛, −¼, −½, −⅞, −1). The resulting codewords are shown in Table 2,with the new code herein called the 5b6w_10_5 code. One embodiment of adriver generating these signal levels is shown as FIG. 22. Each driverslice 1010 produces one wire output signal, with multiple driverelements on each slice being enabled in combination so as to produce the10 distinct output levels required.

TABLE 2 ±[1, ¼, −1/8, ¼, −1/2, −7/8] ±[1, ¼, −1/8, −1/4, −1, ⅛] ±[¼, 1,−1/8, ¼, −1/2, −7/8] ±[¼, 1, −1/8, −1/4, −1, ⅛] ±[½, −1/4, 7 /8, ¼,−1/2, −7/8] ±[½, −1/4, 7 /8, −1/4, −1, ⅛] ±[ −1/4, ½, 7 /8, ¼, −1/2,−7/8] ±[ −1/4, ½, 7 /8, −1/4, −1, ⅛] ±[1, ¼, −1/8, −1/2, ¼, −7/8] ±[1,¼, −1/8, −1, −1/4, ⅛] ±[¼, 1, −1/8, −1/2, ¼, −7/8] ±[¼, 1, −1/8, −1,−1/4, ⅛] ±[½, −1/4, 7 /8, −1/2, ¼, −7/8] ±[½, −1/4, 7 /8, −1, −1/4, ⅛]±[ −1/4, ½, 7 /8, −1/2, ¼, −7/8] ±[ −1/4, ½, 7 /8, −1, −1/4, ⅛]

With this code all comparators as in Eqn. 3 produce output values of +¾.The increase in vertical eye opening compared to the unmodified 5b6wcode is 20*log₁₀((¾)/(⅔))=˜1 dB. The termination power of 5b6w_10_5 isabout 88% of the termination power of the unmodified 5b6w code, so evenat a smaller termination power, 5b6w_10_5 leads to a fractionallyimproved vertical eye opening. However, the implementation cost toobtain this improvement is the added complexity within the transmitterto encode data into an internal representation capable of selectingamong ten rather than four symbol values per wire, and line driverscapable of generating ten discrete output levels rather than four. Sucha transmitter embodiment would be fully compatible with any Glasswingreceiver defined by the matrix of Eqn. 3, and would require less linedriver power than an unmodified 5b6w transmit driver. Because of thisgenerally disadvantageous cost/benefit tradeoff, most embodiments ofGlasswing transmitters are expected to utilize unmodified 5b6w signallevels; where they are cost-effective, alternative embodimentsincorporating the 5b6w_10_5 modifications may transparently beinterchanged and/or interoperate with unmodified ones.

Basic Glasswing Receiver

An embodiment of the Glasswing receiver as defined by the matrix of Eqn.3 is shown in FIG. 14. The six input wires are w₀ through w₅, and thefive sub-channel outputs are S₀ through S₅. In the drawing conventionused here, each of the inputs of the multiple-input comparators 210through 250 is identified by a weight, representing the relativecontribution of that input to the final result output, as defined by thematrix rows of Eqn. 3 defining each MIC. Thus, 210 and 230 may be seento be conventional dual input differential comparators, each having onepositive and one negative input of equal and opposite weight.Comparators 220 and 240 each have two positive inputs each contributingone half to the total positive value, and one input contributing theentire negative value. Comparator 250 has three inputs each contributingone third to the total positive value, and three inputs eachcontributing one third to the total negative value.

Embodiments of the five multi-input comparators corresponding to rowstwo through six of the matrix of Eqn. 3 may use the expandeddifferential pair design of [Holden I] or the alternative design of[Ulrich I]. In some embodiments, Continuous-Time Linear Equalization(CTLE) is also incorporated in the multi-wire comparator stage.Transistor-level schematics of such embodiments suitable for use withGlasswing are described in [Shokrollahi IV] and provided as examplesherein as FIGS. 16 through 20. Each design is shown both with andwithout integrated CTLE and where applicable, alternative embodimentsare illustrated.

The embodiment of FIG. 16 or its alternative embodiment of FIG. 17 issuitable for use as comparator 250 of FIG. 14. The embodiment of FIG. 18or its alternative embodiment of FIG. 19 is suitable for use ascomparator 220, and with the obvious substitution of inputs w0, w1, andw2 with w3, w4, and w5, for use as comparator 240. The embodiment ofFIG. 20 is suitable for use as comparator 210, and with the samesubstitution of inputs, for comparator 230.

In general, Decision Feedback Equalization (DFE) techniques are notrequired in a typical Glasswing embodiment, where the channel length istypically small and signal propagation characteristics good. Nolimitation is implied, however, as DFE and other known art methods maybe combined in a straightforward manner with the described invention. Inat least some such embodiments, DFE is performed not on the receivedwire signals, but instead on the sub-channels. In such configurations,the DFE history and correction computations may be performed on binarysignal values, rather than on quaternary (for 5b6w) or decinary (for5b6w_10_5) wire signals, as would be required where DFE is performeddirectly on wire signals.

Glasswing Transmitter

A variety of known art solutions may be applied to a Glasswingtransmitter, depending on the specific characteristics of thecommunications channel and the process used for fabricating thesemiconductor devices. Extremely short and/or moderate data rateGlasswing channels may utilize high impedance “CMOS-like” point-to-pointinterconnections, which are optimally driven using conventionalvoltage-mode drivers. Higher speed and/or longer channels having matchedimpedance terminations may preferably be driven using current-modedrivers.

It will be apparent to one skilled in the art that the requiredmultilevel output drivers represent a specialized instance ofDigital-to-Analog (D/A) conversion, a well-known field in the art. Thus,the corpus of known methods of D/A conversion, including those based onresistive chains, resistive ladders, summation of regulated voltages orcurrents, or selection among regulated voltages or currents, may be usedin association with the present invention. Regulation may be to absolutevalues, such as a predetermined voltage or current, or may be relativeor proportional to a provided level such as the integrated circuitsupply voltage.

One embodiment of a resistive source terminated driver for a 5b6wtransmitter using the teachings of [Ulrich III] is shown in FIG. 21.Each driver slice 910 produces one wire output signal, with multipledriver elements on each slice being enabled in combination so as toproduce the four distinct output levels which must be generated by thetransmitter, representing the codeword alphabet of +1, +⅓, −⅓, and −1symbols. Thus, as will be obvious to one familiar with the art, theoutput of Encoder in FIG. 21 is comprised of at least two binaryselector signals per driver slice 910, allowing selection of outputvalues representing at least the alphabet of four symbols per wire.Larger alphabets may be utilized as previously described foroptimization of Glasswing receive channel gain by utilizing modifiedmodulation values, at the cost of additional transmitter complexity suchas wider sets of selector signals between the Encoder and the wiredrivers to enable selection of output values representing at least thelarger alphabet set. One embodiment of a driver generating multiplesignal levels is shown as FIG. 22.

Known transmission driver equalization techniques such as Finite ImpulseResponse filtering may be used in combination with Glasswing, asrequired by the particular channel characteristics and system designgoals of the embodiment.

In one embodiment, a method 2300 is described with respect to FIG. 23.At block 2302 a set of information bits is received. At block 2304, areduced-alphabet codeword vector is generated with an encoder. Theencoder forms a weighted sum of sub-channel code vectors wherein aweighting of each sub-channel code vector is based in part on acorresponding antipodal weight determined by a corresponding informationbit in the set of received bits. In various embodiments, the encoder isan orthogonal encoding logic circuit, and it generates areduced-alphabet codeword vector by mapping the received set ofinformation bits to a respective reduced-alphabet codeword vector andoutputting a reduced-alphabet codeword vector selector signal. Theselector signal may then be provided to the plurality of line drivers.Each line driver of the plurality of line drivers uses a portion of thereduced-alphabet codeword vector selector signal to output acorresponding current or voltage representing the reduced-alphabetcodeword vector element. As described previously, the sub-channel codevectors form a reduced-alphabet weight matrix, and they are also aremutually orthogonal and orthogonal to a common mode vector.

At block 2306, the reduced-alphabet codeword vector is transmitted usinga plurality of line drivers. In particular, the reduced-alphabetcodeword vector comprises a plurality of reduced-alphabet codewordvector elements, and each reduced-alphabet codeword vector element istransmitted on a wire of a multi-wire communication bus by a respectiveone of the plurality of line drivers. In some embodiments, thereduced-alphabet codeword vector elements are selected from thenormalized set of elements {+1, +⅓, −⅓, −1}.

The method 2300 may be used with a system having five sub-channelvectors, for use with a six-wire multi-wire communication bus. Theantipodal weights are selected from the normalized set of elements {+1,−1}. Alternative methods may modulate an antipodal weight of at leastone sub-channel according to a clock signal. Further, in someembodiments, a voltage offset may be modeled as including a constantweight applied to the common mode sub-channel vector.

A method 2400 will be described with respect to FIG. 24. At block 2402,a set of signals is received over a multi-wire communications bus. Theset of signals represents a reduced-alphabet codeword vector formed froman antipodal-weighted sum of sub-channel code vectors. At block 2404 aplurality of sub-channel multi-input comparators generates a pluralityof sub-channel output signals. Each multi-input comparator of theplurality of multi-input comparators implements an input weight vectorcorresponding to a sub-channel code vector, and outputs an antipodaloutput signal. At block 2406, a set of information bits is determinedbased on the respective antipodal output signals, such as by slicing theantipodal output signals with respect to a reference value. In oneembodiment, the reduced-alphabet codeword vector elements are from thenormalized set of elements {+1, +⅓, −⅓, −1}, and there are fivesub-channel multi-input comparators, and the multi-wire communicationbus comprises six wires.

Glasswing with Embedded Clock

The embodiment of FIG. 15 utilizes the basic Glasswing receiver of FIG.14, further incorporating an embedded clock signal carried by onesub-channel. Typically, when embedding a clock in a sub-channel, thehighest-amplitude channel is chosen to carry the clock, as taught by[Shokrollahi III]. As a general design practice, this choice generallyresults in the clock channel having the best SNR, and thus the cleanestoutput results.

However, with the modest gain variations seen across the variousGlasswing channels in actual embodiments, there is no significantpractical motivation to select a particular sub-channel for the clockbased on that criterion. In the embodiment of FIG. 15, the sub-channeldefined by the bottom row of the matrix of Eqn. 3 is designated to carrythe clock, as its symmetry and delay characteristics in a practicalembodiment were found to be conducive to integration with thedelay-and-sample behavior of conventional clock/data recovery circuits.One example of such a circuit is shown as 380, being comprised of clockedge detector 382; a fixed, adjustable, or DLL-controlled time delay385, and sample-and-hold or equivalent data samplers 388.

Embodiments

In one embodiment, a method comprises: receiving a set of informationbits; generating a reduced-alphabet codeword vector with an encoder byforming a weighted sum of sub-channel code vectors wherein a weightingof each sub-channel code vector is based in part on a correspondingantipodal weight determined by a corresponding information bit in theset of received bits, and wherein the sub-channel code vectors form areduced-alphabet weight matrix, and are mutually orthogonal andorthogonal to a common mode vector; and, transmitting thereduced-alphabet codeword vector using a plurality of line drivers,wherein the reduced-alphabet codeword vector comprises a plurality ofreduced-alphabet codeword vector elements, and each reduced-alphabetcodeword vector element is transmitted on a wire of a multi-wirecommunication bus by a respective one of the plurality of line drivers.

In one embodiment, the encoder is an orthogonal encoding logic circuit,and generating a reduced-alphabet codeword vector comprises mapping thereceived set of information bits to a respective reduced-alphabetcodeword vector and outputting a reduced-alphabet codeword vectorselector signal.

In one embodiment, the reduced-alphabet codeword vector selector signalis provided to the plurality of line drivers, and wherein each linedriver of the plurality of line drivers uses a portion of thereduced-alphabet codeword vector selector signal to output acorresponding a current or voltage representing the reduced-alphabetcodeword vector element.

In one embodiment, at least one of the sub-channel code vectors has anon-normalized magnitude and wherein the row-wise linear combinations ofthe reduced-alphabet provide a reduced alphabet.

In one embodiment, the reduced-alphabet codeword vector elements areselected from the normalized set of elements {+1, +⅓, −⅓, −1}. There arefive sub-channel vectors, and the multi-wire communication bus comprisessix wires.

In one embodiment, the antipodal weights are selected from thenormalized set of elements {+1, −1}. In one embodiment, an antipodalweight of at least one sub-channel is modulated according to a clocksignal.

In one embodiment, a non-modulated common mode sub-channel vector isincluded to provide a voltage offset.

In one embodiment, sub-channel code vectors having three non-zeroelements comprise a first non-zero element twice as large as each of asecond non-zero element and a third non-zero element, and a position ofthe first non-zero element is aligned to where only one othersub-channel codeword vector has a non-zero element.

In one embodiment, a method comprises: receiving a set of signals over amulti-wire communications bus, the set of signals representing areduced-alphabet codeword vector formed from an antipodal-weighted sumof sub-channel code vectors; generating a plurality of sub-channeloutput signals using a plurality of sub-channel multi-input comparators,each multi-input comparator of the plurality of multi-input comparatorsimplementing an input weight vector corresponding to a sub-channel codevector, and outputting an antipodal output signal; determining a set ofinformation bits from the respective antipodal output signals.

In one embodiment, the method may determine the set of information bitsis done using a plurality of signal slicers. In one embodiment, thereduced-alphabet codeword vector elements are from the normalized set ofelements {+1, +⅓, −⅓, −1}, and there are five sub-channel multi-inputcomparators, and the multi-wire communication bus comprises six wires.

In one embodiment, an apparatus comprises: a plurality of signalconductors for receiving a set of information bits; an encoder connectedto the signal conductors for generating a reduced-alphabet codewordvector by forming a sum of sub-channel code vectors wherein a weightingof each sub-channel code vector is based in part on a correspondingantipodal weight determined by a corresponding information bit in theset of received bits, and wherein the sub-channel code vectors form areduced-alphabet weight matrix, and are mutually orthogonal andorthogonal to a common mode vector; and a plurality of line drivers fortransmitting the reduced alphabet codeword vector, wherein thereduced-alphabet codeword vector comprises a plurality ofreduced-alphabet codeword vector elements, and each reduced-alphabetcodeword vector element is transmitted on a wire of a multi-wirecommunication bus by a respective one of the plurality of line drivers.

In one embodiment, the encoder further comprises a logic circuit thatmaps the received set of information bits to a respectivereduced-alphabet codeword vector and outputs a reduced-alphabet codewordvector selector signal.

In one embodiment, the apparatus includes wire connections for providingthe reduced-alphabet codeword vector selector signal to the plurality ofline drivers, wherein each line driver of the plurality of line driversuses a portion of the reduced-alphabet codeword vector selector signalto output a corresponding a current or voltage representing thereduced-alphabet codeword vector element.

In one embodiment, the encoder is configured to produce areduced-alphabet comprising a set of elements {+1, +⅓, −⅓, −1}. Themulti-wire communications bus comprises six wires to transmit a set offive sub-channel code vectors. In one embodiment, the encoder isconfigured to select the antipodal weights from a set of elements{+1,−1}.

The encoder is configured to modulate at least one sub-channel codevector according to a clock signal. The encoder is configured to providea voltage offset by providing a non-modulated common mode sub-channelvector.

In one embodiment, an apparatus comprises: a multi-wire communicationsbus configured to receive a set of signals, the set of signalsrepresenting a reduced-alphabet codeword vector formed from anantipodal-weighted sum of sub-channel code vectors; a plurality ofsub-channel multi-input comparators, each multi-input comparator of theplurality of multi-input comparators implementing an input weight vectorcorresponding to a sub-channel code vector, and outputting an antipodaloutput signal; a plurality of signal slicers configured to determine aset of information bits from the respective antipodal output signals.

In one embodiment, the apparatus may receive a reduced-alphabet codewordvector elements selected from the normalized set of elements {+1, +⅓,−⅓, −1}, and there are five sub-channel multi-input comparators, and themulti-wire communication bus comprises six wires.

In a further embodiment, a diagnostic tool is provided using a methodcomprising: receiving a plurality of candidate codewords; calculating aratio for each of a plurality of multi-input comparators, of the maximumdistance of an active codeword to a multi-input comparator hyperplanepassing through the origin and the minimum distance of an activecodeword to the multi-input comparator hyperplane passing through theorigin; and exporting the ratio for each central multi-input comparatorfor analysis. Furthermore, the hyperplane may contain an offset and isshifted, and the ratio is the maximum distance of an active codeword tothe shifted hyperplane to the minimum distance of an active codeword tothe shifted hyperplane.

The examples presented herein illustrate the use of vector signalingcodes for point-to-point wire communications. For purposes ofexplanation, interconnection between a first transmitting device and asecond receiving device have been described as unidirectional signalingnetworks. However, this should not been seen in any way as limiting thescope of the described invention. The methods disclosed in thisapplication are equally applicable to networks capable of alternatingsignaling direction (i.e. half duplex), or of providing simultaneouscommunication between separate transmitters and receivers in bothdirections (i.e. full duplex.) Similarly, more than one instance of thedescribed invention may be used essentially in parallel to communicatewider data words and/or provide higher overall communication bandwidth,with individual instances having individual embedded clocks, or two ormore instances sharing a common clock. Other communication mediaincluding optical and wireless communications may similarly be usedrather than the described wire interconnections. Thus, descriptive termsherein such as “voltage” or “signal level” should be considered toinclude equivalents in other measurement systems, such as “opticalintensity”, “RF modulation”, etc. As used herein, the term “physicalsignal” includes any suitable behavior and/or attribute of a physicalphenomenon capable of conveying information. Physical signals may betangible and non-transitory.

1. A method comprising: receiving a set of input signals; generatingsymbols of a normalized-gain codeword based on a weighted sum of a setof subchannels, each subchannel weighted with a corresponding inputsignal, wherein the set of subchannels correspond to rows of a set ofrows selected from an orthogonal matrix, each row of the set of rows (i)mutually orthogonal and (ii) orthogonal to an all-one row; andtransmitting the symbols of the normalized-gain codeword on a multi-wirebus.
 2. The method of claim 1, wherein the orthogonal matrix is anormalized orthogonal matrix.
 3. The method of claim 2, wherein thenormalized orthogonal matrix is represented by the matrix:$\quad\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 \\\frac{3}{8} & {- \frac{3}{8}} & 0 & 0 & 0 & 0 \\\frac{1}{4} & \frac{1}{4} & {- \frac{1}{2}} & 0 & 0 & 0 \\0 & 0 & 0 & \frac{3}{8} & {- \frac{3}{8}} & 0 \\0 & 0 & 0 & \frac{1}{4} & \frac{1}{4} & {- \frac{1}{2}} \\\frac{3}{8} & \frac{3}{8} & \frac{3}{8} & {- \frac{3}{8}} & {- \frac{3}{8}} & {- \frac{3}{8}}\end{matrix}$
 4. (canceled)
 5. The method of claim 1, wherein theorthogonal matrix is an unnormalized matrix, and wherein the methodfurther comprises: generating a normalized set of signals by adjustingsignal levels of the received input signals, and wherein each subchannelis weighted with a corresponding signal of the normalized set ofsignals.
 6. The method of claim 5, wherein the unnormalized matrix isrepresented by the matrix: $\quad\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 0 & 0 & 0 & 0 \\1 & 1 & {- 2} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {- 1} & 0 \\0 & 0 & 0 & 1 & 1 & {- 2} \\1 & 1 & 1 & {- 1} & {- 1} & {- 1}\end{matrix}$
 7. The method of claim 5, wherein adjusting the signallevels of input signals comprises adjusting signal levels oflower-magnitude signals to a magnitude of a highest-magnitude signal ofthe set of input signals.
 8. The method of claim 5, wherein adjustingthe signal levels of input signals comprises adjusting signal levels ofhigher-magnitude signals to a magnitude of a lower-magnitude signal ofthe set of input signals.
 9. The method of claim 1, further comprising:receiving the symbols of the normalized-gain codeword via the multi-wirebus; generating a set of comparator outputs, using a set of multi-inputcomparators (MICs), each comparator output generated based on arespective combination of a respective subset of symbols of thenormalized-gain codeword according to a respective set ofinput-weighting coefficients, and wherein each comparator output has anequal magnitude; and generating a set of output bits by slicing the setof comparator outputs.
 10. The method of claim 9, wherein the respectiveset of input-weighting coefficients corresponds to a respective row ofthe set of rows of a code receiver matrix.
 11. The method of claim 6,wherein the normalized set of input signals are selected from a basisvector [0, ±⅜, ±¼, ±⅜, ±¼, ±⅜].
 12. An apparatus comprising: an encoderconfigured to receive a set of input signals, and to responsivelygenerate symbols of a normalized-gain codeword based on a weighted sumof a set of subchannels, each subchannel weighted with a correspondinginput signal, wherein the set of subchannels correspond to rows of a setof rows selected from an orthogonal matrix, each row of the set of rows(i) mutually orthogonal and (ii) orthogonal to an all-one row; and aplurality of line drivers configured to transmit the symbols of thenormalized-gain codeword on a multi-wire bus.
 13. The apparatus of claim12, wherein the orthogonal matrix is a normalized orthogonal matrix. 14.The apparatus of claim 13, wherein the normalized orthogonal matrix isrepresented by the matrix: $\quad\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 \\\frac{3}{8} & {- \frac{3}{8}} & 0 & 0 & 0 & 0 \\\frac{1}{4} & \frac{1}{4} & {- \frac{1}{2}} & 0 & 0 & 0 \\0 & 0 & 0 & \frac{3}{8} & {- \frac{3}{8}} & 0 \\0 & 0 & 0 & \frac{1}{4} & \frac{1}{4} & {- \frac{1}{2}} \\\frac{3}{8} & \frac{3}{8} & \frac{3}{8} & {- \frac{3}{8}} & {- \frac{3}{8}} & {- \frac{3}{8}}\end{matrix}$
 15. The apparatus of claim 12, wherein the orthogonalmatrix is an unnormalized matrix, and wherein the apparatus furthercomprises: a scaling unit configured to generate a normalized set ofinput signals by adjusting signal levels of the received input signals,and wherein each subchannel is weighted with a corresponding signal ofthe normalized set of input signals.
 16. The apparatus of claim 15,wherein the unnormalized matrix is represented by the matrix:$\quad\begin{matrix}1 & 1 & 1 & 1 & 1 & 1 \\1 & {- 1} & 0 & 0 & 0 & 0 \\1 & 1 & {- 2} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {- 1} & 0 \\0 & 0 & 0 & 1 & 1 & {- 2} \\1 & 1 & 1 & {- 1} & {- 1} & {- 1}\end{matrix}$
 17. The apparatus of claim 16, wherein the normalized setof input signals are selected from a basis vector [0, ±⅜, ±¼, ±⅜, ±¼,±⅜].
 18. The apparatus of claim 15, wherein the scaling unit isconfigured to adjust signal levels of lower-magnitude signals to amagnitude of a highest-magnitude signal of the set of input signals. 19.The apparatus of claim 15, wherein the scaling unit is configured toadjust signal levels of higher-magnitude signals to a magnitude of alower-magnitude signal of the set of input signals.
 20. The apparatus ofclaim 12, further comprising: a plurality of multi-input comparators(MICs) configured to receive the symbols of the normalized-gain codewordvia the multi-wire bus, and to generate a set of comparator outputs,each comparator output generated based on a respective combination of arespective subset of symbols of the normalized-gain codeword accordingto a respective set of input-weighting coefficients, and wherein eachcomparator output has an equal magnitude; and a plurality of slicersconfigured to generate a set of output bits by slicing the set ofcomparator outputs.
 21. The apparatus of claim 20, wherein therespective set of input-weighting coefficients corresponds to arespective row of the set of rows of a code receiver matrix.